In this chapter, we familiarize ourselves with certain aspects of quantum weirdness, namely energy quantization, quantum tunneling, and quantum superposition. To this end, we consider three didactic examples of quantum systems, solve the respective scenario specific Schrödinger equations, and (mathematically and graphically) analyze and interpret the results we obtain therefrom. Despite of the utter simplicity of our scenarios, two of them already defy analytic solutions. Since this is not uncommon when trying to solve Schrödinger equations for specific settings, we also discuss simple numerical methods for Schrödinger equation solving and present code examples which implement those.